# Topics similar to or like Approximations of π

About the history of approximations of ; see also chronology of computation of for a tabular summary. Wikipedia

• Brief chronology of computed numerical values of, or bounds on, the mathematical constant pi. For more detailed explanations for some of these calculations, see Approximations of. Wikipedia

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• Japanese computer scientist and cloud developer advocate at Google. In 2019 Haruka Iwao calculated the world record most accurate value of pi (π); which included 31.4 trillion digits, exceeding the previous record of 22 trillion. Wikipedia

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• Approximate value that has a shorter, simpler, or more explicit representation. For example, replacing \$23.448 with \$23.45, the fraction 312/937 with 1/3, or the expression √2 with 1.414. Wikipedia

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• The mechanical method of algorithmic computation with counting rods in China from the Warring States to Ming dynasty before the counting rods were replaced by the more convenient and faster abacus. Rod calculus played a key role in the development of Chinese mathematics to its height in Song Dynasty and Yuan Dynasty, culminating in the invention Wikipedia

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• In computer science, arbitrary-precision arithmetic, also called bignum arithmetic, multiple-precision arithmetic, or sometimes infinite-precision arithmetic, indicates that calculations are performed on numbers whose digits of precision are limited only by the available memory of the host system. This contrasts with the faster fixed-precision arithmetic found in most arithmetic logic unit (ALU) hardware, which typically offers between 8 and 64 bits of precision. Wikipedia

• Longer than the history of computing hardware and modern computing technology and includes the history of methods intended for pen and paper or for chalk and slate, with or without the aid of tables. Intimately tied to the representation of numbers. Wikipedia

• French mathematician, well known for his contributions to computational mathematics, and for calculating π to 120 decimal places. Son of Pierre Fantet, a royal official in Grenoble, and Jeanne d'Azy, the daughter of a physician from Montpellier. Wikipedia

• Positional decimal numeral system, and is the most common system for the symbolic representation of numbers in the world. Invented between the 1st and 4th centuries by Indian mathematicians. Wikipedia

• Timeline of Hindu history based on the Mahabharata, the Ramayana and the Puranas. Two central dates are the Mahabharata War, which according to this chronology happened at 3534 BCE, and the start of the Kali Yuga, which according to this chronology started at 3508 BCE. Wikipedia

• American multinational software company that provides server, application and desktop virtualization, networking, software as a service , and cloud computing technologies. Citrix products are claimed to be in use by over 400,000 clients worldwide, including 99% of the Fortune 100, and 98% of the Fortune 500. Wikipedia

## Sentences forApproximations of π

• In Proposition II, Archimedes gives an approximation of the value of pi, showing that it is greater than 223⁄71 and less than 22⁄7.
• converges linearly to, adding at least three decimals digits of precision per four terms, a pace slightly faster than the arcsine formula for :
• Being an irrational number, cannot be expressed as a common fraction, although fractions such as 22/7 are commonly used to approximate it.
• These representations led to fast algorithms for computing numerical approximations of.
• This means the scribe of the Moscow Papyrus used to approximate π.
• Tossing a needle 3408 times, he obtained the well-known approximation 355/113 for π, accurate to six significant digits.
• Standard measuring vessels dating to the reign of Wang Mang (9–23 CE) also showed approximations for pi at 3.1590, 3.1497, and 3.167.
• The list contains only formulae whose significance is established either in the article on the formula itself, the article Pi, or the article Approximations of.
• Pi Approximation Day is observed on July 22 (22/7 in the day/month format), since the fraction 22⁄7 is a common approximation of, which is accurate to two decimal places and dates from Archimedes.
• For more detailed explanations for some of these calculations, see Approximations of.
• His other mathematical achievements include deriving an accurate approximation of pi; defining and investigating the spiral that now bears his name; and creating a system using exponentiation for expressing very large numbers.
• In the 14th century, Madhava of Sangamagrama, the founder of the Kerala School of Mathematics, found the Madhava–Leibniz series and obtained from it a transformed series, whose first 21 terms he used to compute the value of π as 3.14159265359.
• He was an expert in the field of dynamics and the approximation of.
• By analogous methods to non-standard analysis one can also use PA to define close approximations to irrational multiples of a non-standard number u such as the least v with v > ⋅ u (these can be defined in PA using non-standard finite rational approximations of even though pi itself cannot be).

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